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## Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions

#### Nihal YOKUŞ [1] , Esra KIR ARPAT [2]

In this paper, we consider the operator L generated in L₂(R₊) by the differential expression

l(y)=-y′′+q(x)y,x∈R₊:=[0,∞)

and the boundary condition

((y′(0))/(y(0)))=α₀+α₁λ+α₂λ²,

where q is a complex valued function and α_{i}∈C,[mbox]<LaTeX>\mbox{\:}</LaTeX>i=0,1,2α₂. We have proved that spectral expansion of L in terms of the principal functions under the condition

q∈AC(R₊),  lim_{x→∞}q(x)=0,  sup[e^{ε√x}|q′(x)|]<∞,  ε>0

taking into account the spectral singularities. We have also proved the convergence of the spectral expansion.
Eigenvalues, spectral singularities, principal functions, resolvent, spectral expansion.
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Primary Language en Articles Orcid: 0000-0002-5327-2312Author: Nihal YOKUŞ Orcid: 0000-0002-6322-5130Author: Esra KIR ARPAT Application Date : November 14, 2017 Acceptance Date : August 6, 2018 Publication Date : August 1, 2019
 Bibtex @research article { cfsuasmas526270, journal = {Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, issn = {1303-5991}, eissn = {2618-6470}, address = {Communications Dergi Editörlüğü Ankara Universitesi Fen Fakültesi 06100 Tandoğan ANKARA}, publisher = {Ankara University}, year = {2019}, volume = {68}, pages = {1316 - 1334}, doi = {10.31801/cfsuasmas.526270}, title = {Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions}, key = {cite}, author = {Yokuş, Nihal and Kır Arpat, Esra} } APA Yokuş, N , Kır Arpat, E . (2019). Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions . Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 68 (2) , 1316-1334 . DOI: 10.31801/cfsuasmas.526270 MLA Yokuş, N , Kır Arpat, E . "Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions" . Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019 ): 1316-1334 Chicago Yokuş, N , Kır Arpat, E . "Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2019 ): 1316-1334 RIS TY - JOUR T1 - Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions AU - Nihal Yokuş , Esra Kır Arpat Y1 - 2019 PY - 2019 N1 - doi: 10.31801/cfsuasmas.526270 DO - 10.31801/cfsuasmas.526270 T2 - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JF - Journal JO - JOR SP - 1316 EP - 1334 VL - 68 IS - 2 SN - 1303-5991-2618-6470 M3 - doi: 10.31801/cfsuasmas.526270 UR - https://doi.org/10.31801/cfsuasmas.526270 Y2 - 2018 ER - EndNote %0 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions %A Nihal Yokuş , Esra Kır Arpat %T Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions %D 2019 %J Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics %P 1303-5991-2618-6470 %V 68 %N 2 %R doi: 10.31801/cfsuasmas.526270 %U 10.31801/cfsuasmas.526270 ISNAD Yokuş, Nihal , Kır Arpat, Esra . "Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 / 2 (August 2019): 1316-1334 . https://doi.org/10.31801/cfsuasmas.526270 AMA Yokuş N , Kır Arpat E . Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.. 2019; 68(2): 1316-1334. Vancouver Yokuş N , Kır Arpat E . Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 2019; 68(2): 1316-1334. IEEE N. Yokuş and E. Kır Arpat , "Spectral expansion of Sturm-Liouville problems with eigenvalue-dependent boundary conditions", Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, pp. 1316-1334, Aug. 2019, doi:10.31801/cfsuasmas.526270

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